I would like to know if anyone knows how a person can obtain a deceased family member's citizenship papers if they don't know the names of that person's parents. Also is there any other way that I can get anything that may have that persons parents names on it, and how do I get it?

As far as I know parent's names aren't required to obtain citizenship papers - it's the information on the person in question that's important. Their full name, dates, proof of death, and if the death is recent proof that you are next-of-kin.

Birth and marriage records would both include the names of parents, and depending upon year of death (after 1907) death records should also include this information if it was known to the informant.